Question

1) Consider the following data for ALL Los Angeles Rams home games for the 2018 NFL season:

Points	Offensive yards
34	432
35	521
38	556
29	416
36	456
54	455
23	407
48	377

a) Compute the points and offensive yards. (2 points)

b) Compute the standard deviation of points and offensive yards. (5 points)

c) Compute the covariance between points and offensive yards. Provide an interpretation of the covariance. (7 points)

d) Compute the correlation coefficient between points and offensive yards. (3 points)

2) Suppose that at a particular university the average GPA is 2.75 and the standard deviation of GPAs is 0.5.

a) Compute the z-score of a student with a GPA of 2.2. (1 points)

b) Compute the z-score of a student with a GPA of 4.0. (1 points)

3) Suppose a city receives precipitation (measured in inches) each year subject to the following probability distribution: X~N(70,49).

a) Compute the probability that the city will receive less than 90 inches in a year. (2 points)

b) Compute the probability that the city will receive more than 60 inches in a year. (2 points)

c) Compute the probability that the city will receive between 49 and 91 inches in a year. (2 points)

4) Consider the following population of individuals along with their corresponding annual income: A earns $30K, B earns $36K, C earns $49 and D earns $60K.

a) Suppose one wants to know the mean annual income of the population and draws a random sample of two individuals (without replacement). List the possible samples and the corresponding sample mean annual income. Also, compute the expected value of the sample mean annual income, E(x). (4 points)

b) Suppose one wants to know the mean annual income of the population and draws a random sample of three individuals (without replacement). List the possible samples and the corresponding sample mean annual income. Also, compute the expected value of the sample mean annual income, E(x). (4 points)

c) How does the larger sample size affect the expected value of the sample means? (2 points)

d) How does the larger sample size affect the dispersion of the possible sample means. (2 points)

Answer 1

a) Sum of points = 297
Sum of offensive yards = 3620

b) Standard deviation measures the deviation of set of data from its mean.

SD of points = 9.8913
SD of offensive yards = 56.6968

3) Variance actually measures the relationship between two or random variable datasets. In simple words, it depicts how the variables are moving with each other.

A negative covariance indicates that they are moving in the opposite direction while a positive one indicates that they are moving in the same direction.

Cov (X, X〉

Covariance = 20.6875

d) The correlation coefficient measures the degree of strength between the set of random variables.

Correlation Co-efficient = 0.04